Method 1: Run a cron job every wednesday. Run your job if `date +%U` is even.
problems: Some years will have 53 wednesdays, so eventually you'll run your job on consecutive weeks.
Method 2: Run a cron job every wednesday. Set a file as a sentinel. If clear, set it and run your job. If set, clear it and dont' run the job.
problems: If the cron job fails to run, your "alternate week" might get out of sync. Someone might screw up the sentinel file.
Pick one based on your needs
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Darren